Structural Conditions of Persistence Under Degradation: Relative Causal Closure and the Limits of Describability

This paper establishes a formal structural result concerning the conditions under which persistence is coherently describable in degradable systems. We introduce a reference-relative notion of causal closure and demonstrate that, for any system subject to irreversible degradation, persistence described within a given causal reference frame necessarily implies the existence of an internal compensatory causal loop accessible in that frame. This closure is shown to be a structural requirement of coherent causal description rather than an ontological claim about the system itself, and it need not be transferable across reference frames. The analysis is conducted in a purely structural and graph-theoretic framework, independent of physical laws, dynamical equations, or empirical observables. The result delineates a fundamental limit of causal describability and establishes a strict distinction between persistence as existence and persistence as a describable property.